A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level

Abstract

We consider a non-Abelian candidate state at filling factor $\nu =3/7$ state belonging to the parton family. We find that, in the second Landau level of GaAs (i.e. at filling factor $\nu =2+3/7$), this state is energetically superior to the standard Jain composite-fermion state and also provides a very good representation of the ground state found in exact diagonalization studies of finite systems. This leads us to predict that \emph{if} a fractional quantum Hall effect is observed at $\nu =3/7$ in the second Landau level, it is likely to be described by this new non-Abelian state. We enumerate experimentally measurable properties that can verify the topological structure of this state.

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Observation of neutral modes in the fractional quantum Hall regime
• Fractional Quantum Hall Effect in the Second Landau Level
• Composite Fermions and Broken Symmetries in Graphene
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Spinful Composite Fermions in a Negative Effective Field
• Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study
• Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems

Cited by in corpus (3)

• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$